# A certain dielectric, with adielectric constant 23...

A certain dielectric, with adielectric constant 23, can withstand an electric field of 5*10^7 V/m. Suppose we want to use thisdielectric to construct a 0.3 ? F capacitor thatcan withstand a potential difference of 2400 V. The permittivity offree space is 8.85 * 10^-12 C^2 /N * m^2.

1. What is the minimum plate separation? Answer in units of? m.

2. What must the area of the plates be?Answer in units of m^2.

## Answers ( 1 )

1. The capacitance of the capacitor that is to be constructedis C=0.3 ? F
This could be withstand a potential difference V=2400V
?The charge that can store is Q=CxV
=0.3x10-6 x 2400
=720x10-6 coulombs
But we can have E =Q/(k? 0 A )   fromGauss' law
?A=Q/kE? 0                             =720x10-6/ (23 x 5x107 x 8.85 x 10-12)
=0.707 x 10 -1
=0.0707 m2
Now we have C=k? 0 A/d
?d=k? 0 A/C

=23 x 8.85 x 10 -12 x .0707 / (0.3x10-6 )
=47.96x10-6m
=47.96  ?m
Therefore the minimum platesepatation should be 47.96  ? m